Green, as a political newcomer, was elected to the Alaska Senate in 1994, defeating a 22-year Democratic incumbent in a district representing most of the population of the Matanuska-Susitna Borough.
She was first elected in 1994 by defeating Democratic incumbent Jalmar M. "Jay" Kerttula, who was the longest-serving member in the history of the Alaska Legislature.
Kerttula was long regarded as vulnerable, and was re-elected in 1984 with under 52% of the vote just as the Matanuska-Susitna Borough was starting to trend Republican.
Given the political atmosphere at the time, Green benefited from being a first-time candidate running against an incumbent who had been in office for over 30 years.
They had three children; their daughter, Kristie, married Tuckerman Babcock, a state official and former chairman of the Alaska Republican Party.